In the UK we have the Amateur Martial Association (AMA), where in order to be recognised as an instructor with them you
Well no, 'we' don't have it. It is one of many businesses that organise insurance, certificates, grading books and advise on things like health and safety, child protection agencies etc. They don't recognise all instructors only those that pay to use them. There are many other organisations that do the same, none of them are authorities that can recognise instructors as being 'qualified' other than because the instructors above them say they are or they pay to register. Other organisations which are the same are NAKMAS, FEKO, BMABA, WMIAA, UKASKO,WAKO,BCA, etc etc.
Your instructors have signed up with AMA, it doesn't mean they are actually qualified instructors I'm afraid just that they chose to join that business to get their insurance etc.